Geometry Semester 1 Exam Study Guide

Geometry Semester 1 Exam Study GuideName Date BlockPreparing for the Semester Exam Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of thenotes, reprint them from my web page (under Class Summary). Use the flashcardslocated at -1-exam-review-flashcards/ to help review terms, definitions, and concepts. DON’T LIMIT STUDYING TOPRACTICE PROBLEMS IN THIS STUDY GUIDE.Know: Logico terms: inductive reasoning, deductive reasoning, conjecture, counterexample,conditional statement, hypothesis, conclusion, negation, converse, inverse,contrapositive, Law of Detachment, Law of Syllogismo Be able to form converse/inverse/contrapositive statements from a given statemento Be able to determine if statements are equivalent (have same truth value)o Review using Venn (Euler) Diagrams to deductively draw conclusions Basicso terms: point, line, plane, collinear, coplanar, axioms, postulates, theorems,midpoint, bisector, angles (obtuse, acute, right, complementary, supplementary,vertical, linear pair)o Be able to apply midpoint and distance formulas: x x y y Midpoint M of points (x1, y1) and (x2, y2) M 1 2 , 1 2 2 2 Given points A(x1, y1) and B(x2, y2) are points on the coordinate plane, then thedistance between A and B is: AB (x 2 x1 ) 2 (y2 y1 ) 2o Be able to classify angles as acute, obtuse, or right, and find angle measures forcomplementary, supplementary, and vertical angles.Parallel Lineso Given a transversal crossing two lines, be able to identify angles that are interior,exterior, alternate, consecutive, corresponding, alternate interior, alternate exterior,and consecutive interior. Know which angles are congruent or supplementary if thetransversal crosses two parallel lines.o Slope: be able to find the slope given a linear equation in two variables Be able to write equations of lines given two points, or a point and a slope point-slope formula: y – y1 m(x – x1) parallel lines have the same slope but different y-intercepts perpendicular lines have slopes whose product is -1 (negative reciprocals of eachother) Given a line, be able to write the equation of another line that is either parallel orperpendicular to the given line through a point on the new lineo Know how to apply parallel/perpendicular line theoremsTriangleso Congruent triangles : Triangles may be proven congruent if all corresponding parts (angles and sides)are congruent; or the following postulates/theorems may be used: SSS, SAS, ASA, AAS, HL

Geometry Semester 1 Exam Study GuidePage 2Triangles may NOT be proven congruent if all we know is AAA or SSACorresponding parts of congruent triangles are congruent (CPCTC)Be able to identify whether triangles are congruent or whether correspondingparts are congruent (find triangle congruence first) Be able to supply statements or reasons given a triangle congruence proof Be able to apply theorems/postulates associated with isosceles triangles (such asthe base angles theorem)o Triangle Inequalities: Be able to order the sides or angles of triangle by size Be able to determine if three side lengths can form a triangle Given two side lengths of a triangle, give a range of possible values for the thirdside Be able to apply the Hinge Theorem to determine which angles or sides of atriangle are bigger or smaller than in another triangle.o Triangle Similarity: Be able to solve proportions. Be able to solve problems using extended ratios (e.g. finding triangle anglemeasures) Be able to find geometric means: the geometric mean of a and b is given by ab Be able to find scale factor of similar triangles, and apply to find missing sides ina similar triangles, and to find perimeters of similar triangles. Be able to prove similarity using AA, SSS, and SAS postulates/theorems.o Right Triangles Use the Pythagorean Theorem to find a missing side of a right triangle. Determine if three sides make a triangle, and, if so, is the triangle right, acute, orobtuse. Find missing sides of a triangle given a right triangle with an altitude drawnthrough the right angle to the other side (use geometric mean). Find missing sides of special right triangles (45-45-90 or 30-60-90). Be able to apply trigonometry ratios (SOH CAH TOA) and inverse trig to findmissing sides or angles of triangles. Practice Questions1) Given the statement "If it is Monday, then we have art class," write the converse,inverse and contrapositive of the statement. Assuming the initial statement is true,what are the truth values of the other statements?2) What is the inverse of the statement "If 4 x 8 then x 2 "?a) If x 2 then 4 x 8b) If x 2 then 4 x 8c) If x 2 then 4 x 8d) If 4 x 8 then x 2

Geometry Semester 1 Exam Study GuidePage 33) Assuming these statements are true:Some athletes are fast runners.All fast runners like chocolate.Which of the following is a valid conclusion?a) All fast runnersare athletes.b) All athletes likechocolate.c) Some fast runners donot like chocolate.d) Some athleteslike chocolate.4) According to the Venn diagram at right, which is true?There may be more than one correct answer.a) Some musicians play only brass.b) No musicians play both strings and brass.c) All musicians play strings.d) Some musicians play brass and strings.5) Consider the following statements:p: The sum of three angles is 180oq: The three angles can form a triangle.Which of the following is a symbolic representation of the statement:If three angles cannot form a triangle, then the sum of the angles is not 180o.a) p qb) q pc) p qd) q p6) Consider the following arguments. If the first two statements are true, in whichargument is the third statement an invalid conclusion? There may be more than onecorrect answer.a) If it snows, then we will not have school.If we do not have school, we will not have a test.If we did not have a test, then it snowed.b) If Mary does her homework, she will get an A.If Mary gets an A, she will not be punished.If Mary is punished, then she did her homework.c) If you pass the test, you will get a gold star.If you get a gold star, you will get a certificate.If you did not get a certificate, then you did not pass the test.d) If Bobby cleans his room, then he will get his allowance.If Bobby gets his allowance, he will buy a video game.If Bobby cleans his room, then he will buy a video game.

Geometry Semester 1 Exam Study GuidePage 47) Based strictly on the diagram at right, which is a validconclusion? There may be more than one correctanswer.a) Some science fiction novels are also romance novels.b) No science fiction novel is also a mystery.c) No mysteries are also romance novels.d) No romance novels are also science fiction.8) If p represents: the remainder of x 2 is 0 and q represents: x is an even number,which is a symbolic representation of:If the remainder of x 2 is not 0 then x is not even.a) p qb) q pc) p qd) q p9) What is the midpoint of the segment joining (12, 2) and (-5, -7)?a) (9, 17)b) (5, -3)c) (8.5, 4.5)d) (3.5, -2.5)10) The coordinates of the midpoint of AB are (-2, 1), and the coordinates of A are (2, 3).What are the coordinates of B?a) (0, 2)b) (-1, 2)c) (-3, 4)11) What are the coordinates of the midpoint of XY ?a) (-0.5, 4)b) (3.5, 4)c) (-3, 1.5)d) (0.5, -0.5)12) Using the same diagram as the previous question, whatis the length of XY to the nearest tenth?a) 4.1b) 8.1c) 3.9d) 9.213) If line a is parallel to line b, what is m 1?a) 40ob) 50oc) 90od) 140o14) Line a is parallel to line b if (there may bemore than one correct answer)a) m 1 m 8b) m 3 m 6c) m 4 m 5d) m 3 m 2d) (-6, -1)

Geometry Semester 1 Exam Study GuidePage 515) George used a decorative fencing to enclose hisdeck. Using the information on the diagram andassuming the top and bottom are parallel, m x is:a) 50ob) 80oc) 100od) 130o16) Line l intersects lines w, x, y, and z. Whichtwo lines are parallel?a) w and xb) w and yc) x and zd) y and z17) BA is parallel to CD if:a) m 1 m 2b) m 3 m 4c) m 1 m 2 90d) m 1 m 2 m 3 m 418) The measure of YZV is 40o and the measure of XYZ is 65o.Which of these angles must measure 40o in order for VR to beparallel to YZ ?a) YVZb) ZVRc) ZYVd) VRX19) What value of x will show that lines l and m areparallel?a) 42b) 96c) 30d) 620) Angle 1 is a complement of angle 2. If m 1 14x 8 and m 2 8x 6 , what is the valueof x and of m 1?

Geometry Semester 1 Exam Study GuidePage 621) What is m 3 ?a) 65ob) 75oc) 85od) 90o22) Two angles of a triangle measure 89o and 32o. Classify the triangle by its sides andangles.a) isosceles rightb) scalene acutec) equilateralequiangulard) scalene obtuse23) Which of the following equations represent a line with slope -5 and passes throughpoint (1, -2)?a) 5x – y 3b) -5x y 3c) 5x y 3d) 5x y -324) What is the slope of the line in the graph at right?a)13b)23c) 2d) 325) Write an equation of the line perpendicular to the lineshown in the graph at right (same as the previousquestion) and that passes through the point (-4, -3) onthe perpendicular line.26) In ABC , D is the midpoint of AB and E is the midpoint of BC . If AC 3x 15 andDE 6 , what is the value of x?27) What is the slope of the line perpendicular to 7 x 3 y 10 ?a)73b)37c) 73d) 3728) What is the slope of a line parallel to the line formed by connecting coordinates (-1, 5)and (7, -3)?a) 1b) -1c) 14d) 43

Geometry Semester 1 Exam Study GuidePage 729) If ACB CAD , what is the value of x and y?30) Which two points determine a line parallel to QR ?a) 2, 1 and 2, - 1 b) 1, 4 and 5, 2 c) 1, - 1 and 2, - 3 d) 1, 1 and 2, - 1 31) The line formed by points (5, 1), (-2, 6) and the line formed by points (-3, 10) , (2,3)are a) parallelb) perpendicularc) not parallel orperpendiculard) unable to determine whether theyare parallel or perpendicular32) Given: AC BD , AD BCWhich could be used to prove DCA CDB ?a) SSSb) SASc) ASAd) AAS33) Given: AE and BD bisect each other at C.Which could be used to prove ABC EDC ?a) SSSb) SASc) ASAd) AAS34) Which of the following could be the lengths of the sides of ABC ?a) AB 12, BC 15, AC 2b) AB 9, BC 15, AC 4c) AB 150, BC 100, AC 50d) AB 10, BC 8, AC 1235) In ABC , m B 59 and m C 57 . From shortest to longest, the sides of ABC are:a) AC, BC, ABb) AB, BC, ACc) BC, AC, ABd) AB, AC, BC

Geometry Semester 1 Exam Study GuidePage 836) On a map, cities Binghamton, Endicott, and Johnson City form a triangle. Endicott is70 miles away from Binghamton, and Johnson City is 90 miles from Binghamton.Which is a possible distance from Endicott to Johnson City?a) 5 milesb) 10 milesc) 150 milesd) 200 miles37) Triangles ABC and DEF are similar and have measurements as shown. What is EF?a)212b)152c)92d)3238) Given: AXY ABC AYX ACBWhich is a true proportion? There may be more than one correctanswer.a)AX AY XY AB AC BCb)AX AY XY XB YC BCc)AB AC BC AX AY XYd)AX AC XY AB AY BC39) The ratio of the perimeter of U to the perimeter of V is 1:2. If the triangles are similar, what is thevalue of x y?a) 3b) 6c) 12d) 1840) ABC EFG . What is the perimeter of EFG ?a) 21b) 24c) 36d) 4241) The geometric mean of 8 and 10 is:a) 9b) 40c) 4 5d) 5 442) In right triangle ABC shown in the diagram, altitudeBD is drawn to hypotenuse AC , CD 12, and AD 3.What is the length of BD and AB ? Answer in simplestradical form.

Geometry Semester 1 Exam Study GuidePage 943) Using the figure out at right, find x, y, and z. Then findthe perimeter of the figure.44) The figure at right shows ABC, which is a right triangle withaltitude AD drawn ( AD BC ). Find the values of a, e, d, and f.45) The support legs on a bench are attached in such a way that the angle made by onewith the ground is 130o. What must the measure of theangle marked x be in order for the seat of the bench to beparallel to the ground?46) Which triangle is not congruent to the other threetriangles?a)b)c)d)47) Mr. Anderson is constructing a walkway through his rectangular garden. The walkwayruns diagonally as shown in the diagram. To the nearesttenth, what is the length of the walkway?